메뉴 건너뛰기




Volumn 282, Issue 11, 2009, Pages 1492-1512

A variational characterization of rate-independent evolution

Author keywords

Maximal dissipation; Rate independent evolution; Variational principle

Indexed keywords


EID: 76849093177     PISSN: 0025584X     EISSN: 15222616     Source Type: Journal    
DOI: 10.1002/mana.200810803     Document Type: Article
Times cited : (32)

References (40)
  • 2
    • 43949142447 scopus 로고    scopus 로고
    • A rate-independent model for the isothermal quasi-static evolution of shapememory materials
    • F. Auricchio, A. Mielke, and U. Stefanelli, A rate-independent model for the isothermal quasi-static evolution of shapememory materials, Math. Models Meth. Appl. Sci. 18, No. 1, 125-164 (2008).
    • (2008) Math. Models Meth. Appl. Sci. , vol.18 , Issue.1 , pp. 125-164
    • Auricchio, F.1    Mielke, A.2    Stefanelli, U.3
  • 3
    • 41549084999 scopus 로고    scopus 로고
    • The variational approach to fracture, J
    • B. Bourdin, G. A. Francfort, and J.-J. Marigo, The variational approach to fracture, J. Elasticity 91, No. 1-3, 5-148 (2008).
    • (2008) Elasticity , vol.91 , Issue.1-3 , pp. 5-148
    • Bourdin, B.1    Francfort, G.A.2    Marigo, J.-J.3
  • 4
    • 0033411059 scopus 로고    scopus 로고
    • Variational formulation of softening phenomena in fracture mechanics: the one-dimensional case
    • A. Braides, G. Dal Maso, and A. Garroni, Variational formulation of softening phenomena in fracture mechanics: the one-dimensional case, Arch. Ration. Mech. Anal. 146, No. 1, 23-58 (1999).
    • (1999) Arch. Ration. Mech. Anal. , vol.146 , Issue.1 , pp. 23-58
    • Braides, A.1    Dal Maso, G.2    Garroni, A.3
  • 5
    • 47749102155 scopus 로고    scopus 로고
    • A vanishing viscosity approach to fracture growth in a cohesive zone model with prescribed crack path
    • F. Cagnetti, A vanishing viscosity approach to fracture growth in a cohesive zone model with prescribed crack path, Math. Models Methods Appl. Sci. 18, No. 7, 1027-1071 (2008).
    • (2008) Math. Models Methods Appl. Sci. , vol.18 , Issue.7 , pp. 1027-1071
    • Cagnetti, F.1
  • 6
    • 33644607451 scopus 로고    scopus 로고
    • Quasistatic evolution problems for linearly elastic-perfectly plastic materials
    • G. Dal Maso, A. DeSimone, and M. G. Mora, Quasistatic evolution problems for linearly elastic-perfectly plastic materials, Arch. Ration. Mech. Anal. 180, No. 2, 237-291 (2006).
    • (2006) Arch. Ration. Mech. Anal. , vol.180 , Issue.2 , pp. 237-291
    • Dal Maso, G.1    DeSimone, A.2    Mora, M.G.3
  • 7
    • 56849088495 scopus 로고    scopus 로고
    • Globally stable quasistatic evolution in plasticity with softening
    • G. Dal Maso, A. DeSimone, M. G. Mora, and M. Morini, Globally stable quasistatic evolution in plasticity with softening, Netw. Heterog. Media 3, No. 3, 567-614 (2008).
    • (2008) Netw. Heterog. Media , vol.3 , Issue.3 , pp. 567-614
    • Dal Maso, G.1    DeSimone, A.2    Mora, M.G.3    Morini, M.4
  • 8
    • 46749094568 scopus 로고    scopus 로고
    • A vanishing viscosity approach to quasistatic evolution in plasticity with softening
    • G. Dal Maso, A. DeSimone, M. G. Mora, and M. Morini, A vanishing viscosity approach to quasistatic evolution in plasticity with softening, Arch. Ration. Mech. Anal. 189, No. 3, 469-544 (2008).
    • (2008) Arch. Ration. Mech. Anal. , vol.189 , Issue.3 , pp. 469-544
    • Dal Maso, G.1    DeSimone, A.2    Mora, M.G.3    Morini, M.4
  • 9
    • 17744387968 scopus 로고    scopus 로고
    • Quasistatic crack growth in nonlinear elasticity
    • G. Dal Maso, G. A. Francfort, and R. Toader, Quasistatic crack growth in nonlinear elasticity, Arch. Ration. Mech. Anal. 176, No. 2, 165-225 (2005).
    • (2005) Arch. Ration. Mech. Anal. , vol.176 , Issue.2 , pp. 165-225
    • Dal Maso, G.1    Francfort, G.A.2    Toader, R.3
  • 10
    • 33645145027 scopus 로고    scopus 로고
    • On the rate-independent limit of systems with dry friction and small viscosity
    • M. A. Efendiev and A. Mielke, On the rate-independent limit of systems with dry friction and small viscosity, J. Convex Anal. 13, No. 1, 151-167 (2006).
    • (2006) J. Convex Anal. , vol.13 , Issue.1 , pp. 151-167
    • Efendiev, M.A.1    Mielke, A.2
  • 11
    • 67649548111 scopus 로고    scopus 로고
    • A vanishing viscosity approach to a quasistatic evolution problem with nonconvex energy
    • to appear
    • A. Fiaschi, A vanishing viscosity approach to a quasistatic evolution problem with nonconvex energy, Ann. Inst. H. Poincaré Anal. Non Linéaire (2009), to appear.
    • (2009) Ann. Inst. H. Poincaré Anal. Non Linéaire
    • Fiaschi, A.1
  • 12
    • 33745513030 scopus 로고    scopus 로고
    • Existence results for a class of rate-independent material models with nonconvex elastic energies
    • G. Francfort and A. Mielke, Existence results for a class of rate-independent material models with nonconvex elastic energies, J. Reine Angew. Math. 595, 55-91 (2006).
    • (2006) J. Reine Angew. Math. , vol.595 , pp. 55-91
    • Francfort, G.1    Mielke, A.2
  • 13
    • 0032139947 scopus 로고    scopus 로고
    • Revisiting brittle fracture as an energy minimization problem, J. Mech
    • G. A. Francfort and J.-J. Marigo, Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids 46, No. 8, 1319-1342 (1998).
    • (1998) Phys. Solids , vol.46 , Issue.8 , pp. 1319-1342
    • Francfort, G.A.1    Marigo, J.-J.2
  • 15
    • 0017931943 scopus 로고
    • On plasticity with hardening
    • C. Johnson, On plasticity with hardening, J. Math. Anal. Appl. 62, No. 2, 325-336 (1978).
    • (1978) J. Math. Anal. Appl. , vol.62 , Issue.2 , pp. 325-336
    • Johnson, C.1
  • 16
    • 53049087113 scopus 로고    scopus 로고
    • On the inviscid limit of a model for crack propagation
    • D. Knees, A. Mielke, and C. Zanini, On the inviscid limit of a model for crack propagation, Math. Models Methods Appl. Sci. 18, No. 9, 1529-1568 (2008).
    • (2008) Math. Models Methods Appl. Sci. , vol.18 , Issue.9 , pp. 1529-1568
    • Knees, D.1    Mielke, A.2    Zanini, C.3
  • 17
    • 33746077721 scopus 로고    scopus 로고
    • A rate-independent approach to the delamination problem, Math
    • M. Kočvara, A. Mielke, and T. Roubíček, A rate-independent approach to the delamination problem, Math. Mech. Solids 11, No. 4, 423-447 (2006).
    • (2006) Mech. Solids , vol.11 , Issue.4 , pp. 423-447
    • Kočvara, M.1    Mielke, A.2    Roubíček, T.3
  • 18
    • 84867925391 scopus 로고    scopus 로고
    • Rate independent Kurzweil processes
    • P. Krejčí and M. Liero, Rate independent Kurzweil processes, Appl. Math. 54, No. 2, 117-145 (2009).
    • (2009) Appl. Math. , vol.54 , Issue.2 , pp. 117-145
    • Krejčí, P.1    Liero, M.2
  • 19
    • 76849086337 scopus 로고    scopus 로고
    • Epsilon-stable quasi-static brittle fracture evolution, Comm
    • to appear
    • C. J. Larsen, Epsilon-stable quasi-static brittle fracture evolution, Comm. Pure Appl. Math. (2009), to appear.
    • (2009) Pure Appl. Math
    • Larsen, C.J.1
  • 20
    • 0042360574 scopus 로고    scopus 로고
    • Energetic formulation of multiplicative elasto-plasticity using dissipation distances, Contin
    • A. Mielke, Energetic formulation of multiplicative elasto-plasticity using dissipation distances, Contin. Mech. Thermodyn. 15, No. 4, 351-382 (2003).
    • (2003) Mech. Thermodyn. , vol.15 , Issue.4 , pp. 351-382
    • Mielke, A.1
  • 21
    • 14944350933 scopus 로고    scopus 로고
    • Existence of minimizers in incremental elasto-plasticity with finite strains
    • (electronic)
    • A. Mielke, Existence of minimizers in incremental elasto-plasticity with finite strains, SIAM J. Math. Anal. 36, No. 2, 384-404 (2004) (electronic).
    • (2004) SIAM J. Math. Anal. , vol.36 , Issue.2 , pp. 384-404
    • Mielke, A.1
  • 22
    • 66049141597 scopus 로고    scopus 로고
    • Evolution of rate-independent systems
    • C. Dafermos and E. Feireisl, editors, Elsevier, Amsterdam
    • A. Mielke, Evolution of rate-independent systems, in: C. Dafermos and E. Feireisl, editors, Handbook of Differential Equations, Evolutionary Equations Vol. 2 (Elsevier, Amsterdam, 2005), pp. 461-559.
    • (2005) Handbook of Differential Equations, Evolutionary Equations , vol.2 , pp. 461-559
    • Mielke, A.1
  • 23
    • 46749100683 scopus 로고    scopus 로고
    • A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems, ESAIM Control Optim
    • A. Mielke and M. Ortiz, A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems, ESAIM Control Optim. Calc. Var. 14, No. 3, 494-516 (2008).
    • (2008) Calc. Var. , vol.14 , Issue.3 , pp. 494-516
    • Mielke, A.1    Ortiz, M.2
  • 24
    • 70349869188 scopus 로고    scopus 로고
    • Modeling solutions with jumps for rate-independent systems on metric spaces, Discrete Contin
    • A. Mielke, R. Rossi, and G. Savaré, Modeling solutions with jumps for rate-independent systems on metric spaces, Discrete Contin. Dyn. Syst. 25, 585-615 (2009).
    • (2009) Dyn. Syst. , vol.25 , pp. 585-615
    • Mielke, A.1    Rossi, R.2    Savaré, G.3
  • 25
    • 85018392517 scopus 로고    scopus 로고
    • A rate-independent model for inelastic behavior of shape-memory alloys
    • (electronic)
    • A. Mielke and T. Roubíček, A rate-independent model for inelastic behavior of shape-memory alloys, Multiscale Model. Simul. 1, No. 4, 571-597 (2003) (electronic).
    • (2003) Multiscale Model. Simul. , vol.1 , Issue.4 , pp. 571-597
    • Mielke, A.1    Roubíček, T.2
  • 26
    • 32644446311 scopus 로고    scopus 로고
    • Rate-independent damage processes in nonlinear elasticity, Math
    • A. Mielke and T. Roubíček, Rate-independent damage processes in nonlinear elasticity, Math. Models Methods Appl. Sci. 16, No. 2, 177-209 (2006).
    • (2006) Models Methods Appl. Sci. , vol.16 , Issue.2 , pp. 177-209
    • Mielke, A.1    Roubíček, T.2
  • 27
    • 37349110656 scopus 로고    scopus 로고
    • Γ-limits and relaxations for rate-independent evolutionary problems
    • A. Mielke, T. Roubíček, and U. Stefanelli, Γlimits and relaxations for rate-independent evolutionary problems, Calc. Var. Partial Differ. Equ. 31, No. 3, 387-416 (2008).
    • (2008) Calc. Var. Partial Differ. Equ. , vol.31 , Issue.3 , pp. 387-416
    • Mielke, A.1    Roubíček, T.2    Stefanelli, U.3
  • 28
    • 67949112197 scopus 로고    scopus 로고
    • A discrete variational principle for rate-independent evolution
    • A. Mielke and U. Stefanelli, A discrete variational principle for rate-independent evolution, Adv. Calc. Var. 1, No. 4, 399-431 (2008).
    • (2008) Adv. Calc. Var. , vol.1 , Issue.4 , pp. 399-431
    • Mielke, A.1    Stefanelli, U.2
  • 29
    • 0002902403 scopus 로고    scopus 로고
    • A mathematical model for rate-independent phase transformations with hysteresis
    • edited by H.-D. Alber, R. Balean, and R. Farwig Shaker-Verlag, Aachen
    • A. Mielke and F. Theil, A mathematical model for rate-independent phase transformations with hysteresis, in: Proceedings of the workshop on " Models of Continuum Mechanics in Analysis and Engineering" , edited by H.-D. Alber, R. Balean, and R. Farwig (Shaker-Verlag, Aachen, 1999), pp. 117-129.
    • (1999) Proceedings of the workshop on "Models of Continuum Mechanics in Analysis and Engineering" , pp. 117-129
    • Mielke, A.1    Theil, F.2
  • 30
    • 3042535426 scopus 로고    scopus 로고
    • On rate-independent hysteresis models, NoDEA
    • A. Mielke and F. Theil, On rate-independent hysteresis models, NoDEA, Nonlinear Diff. Equ. Appl. 11, 151-189 (2004).
    • (2004) Nonlinear Diff. Equ. Appl. , vol.11 , pp. 151-189
    • Mielke, A.1    Theil, F.2
  • 31
    • 0036012128 scopus 로고    scopus 로고
    • A variational formulation of rate-independent phase transformations using an extremum principle
    • A. Mielke, F. Theil, and V. I. Levitas, A variational formulation of rate-independent phase transformations using an extremum principle, Arch. Ration. Mech. Anal. 162, No. 2, 137-177 (2002).
    • (2002) Arch. Ration. Mech. Anal. , vol.162 , Issue.2 , pp. 137-177
    • Mielke, A.1    Theil, F.2    Levitas, V.I.3
  • 32
    • 33746271617 scopus 로고    scopus 로고
    • An energetic material model for time-dependent ferroelectric behavior: existence and uniqueness
    • A. Mielke and A. M. Timofte, An energetic material model for time-dependent ferroelectric behavior: existence and uniqueness, Math. Models Appl. Sci. 29, 1393-1410 (2005).
    • (2005) Math. Models Appl. Sci. , vol.29 , pp. 1393-1410
    • Mielke, A.1    Timofte, A.M.2
  • 33
    • 76849088526 scopus 로고    scopus 로고
    • A comparative analysis on variational models for quasi-static brittle crack propagation, Preprint Available at
    • M. Negri, A comparative analysis on variational models for quasi-static brittle crack propagation, Preprint (2008). Available at: http://cvgmt.sns.it/
    • (2008)
    • Negri, M.1
  • 34
    • 57249114626 scopus 로고    scopus 로고
    • Quasi-static crack propagation by Griffith's criterion, Math
    • to appear
    • M. Negri and C. Ortner, Quasi-static crack propagation by Griffith's criterion, Math. Models Meth. Appl. Sci, to appear (2008).
    • (2008) Models Meth. Appl. Sci.
    • Negri, M.1    Ortner, C.2
  • 35
    • 77949273779 scopus 로고    scopus 로고
    • Proceedings of the 6th AIMS International Conference on Dynamical Systems and Differential Equations, Poitiers 2006, Discrete Contin. Dyn. Syst. Supplement
    • T. Roubíček, Modelling of thermodynamics of martensitic transformation in shape-memory alloys, in: Proceedings of the 6th AIMS International Conference on Dynamical Systems and Differential Equations, Poitiers 2006, Discrete Contin. Dyn. Syst. Supplement, 892-902 (2007).
    • (2007) Modelling of thermodynamics of martensitic transformation in shape-memory alloys , pp. 892-902
    • Roubíček, T.1
  • 36
    • 63849180600 scopus 로고    scopus 로고
    • Proceedings of the MFO Workshop: Analysis and Numerics for Rate-independent Processes, Oberwolfach Reports (Forschungsinstitut Oberwolfach, European Mathematical Society
    • U. Stefanelli, A variational principle in non-smooth mechanics, in: Proceedings of the MFO Workshop: Analysis and Numerics for Rate-independent Processes, Oberwolfach Reports Vol. 4 (Forschungsinstitut Oberwolfach, European Mathematical Society, 2007), pp. 622-624.
    • (2007) A variational principle in non-smooth mechanics , vol.4 , pp. 622-624
    • Stefanelli, U.1
  • 37
    • 63849300447 scopus 로고    scopus 로고
    • A variational principle for hardening elasto-plasticity
    • U. Stefanelli, A variational principle for hardening elasto-plasticity, SIAM J. Math. Anal. 40, No. 2, 623-652 (2008).
    • (2008) SIAM J. Math. Anal. , vol.40 , Issue.2 , pp. 623-652
    • Stefanelli, U.1
  • 38
    • 0013482532 scopus 로고
    • Existence et régularité des solutions des équations de la plasticité
    • Thèse de 3ème cycle, Université Paris VI
    • P.-M. Suquet, Existence et régularité des solutions des équations de la plasticité, C. R. Acad. Sci. Paris Sér. A 286, 1201-1204 (1978); Thèse de 3ème cycle, Université Paris VI (1978).
    • (1978) C. R. Acad. Sci. Paris Sér. A , vol.286 , pp. 1201-1204
    • Suquet, P.-M.1
  • 39
    • 60749102423 scopus 로고    scopus 로고
    • An artificial viscosity approach to quasistatic crack growth
    • R. Toader and C. Zanini, An artificial viscosity approach to quasistatic crack growth, Boll. Unione Mat. Ital. (9) 2, No. 2, 1-35 (2009).
    • (2009) Boll. Unione Mat. Ital. (9) , vol.2 , Issue.2 , pp. 1-35
    • Toader, R.1    Zanini, C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.